Answer to Question #183785 in Macroeconomics for Aaa

Question

Design a government intervention in the competitive equilibrium that could restore social efficiency. In particular, a tax τ on production f (n) is imposed on the firms which is rebated lump-sum to the households. As a first step, set up the new firms maximization with the tax, as well as the maximization problem of the households and derive the respective first-order conditions. Show that leisure demand with taxes is given by l2nd = γ(1−pδ) . Then, determine the optimal size (1−τ)+γ(1−pδ) of the tax τ that would establish equivalence between the competitive equilibrium and Social Planner allocations. 

Households utility:U(c, l) = ln(c − pE) + γ ln l, and the budget constraint is c = w(1 − l). 

Externalities: E = δY

Firms produce with a linear technology using only labor input n: Y = f (n) = n.

Assume that 0 < δp < 1 

Answer 1

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